Finite Group Databasebeta

← #29590318

Subgroups — #29590318

Order 15616.

452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449090C211yesmaximal, characteristic
2#21445556C211yesmaximal, characteristic
3#21444132C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic, complemented
5#21443847C211yesmaximal, characteristic, complemented
6#21443845C211yesmaximal, characteristic, complemented
7C61×#1354C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×Q8×Dic61C411yescharacteristic
10C2×#14519735C2211yescharacteristic
11#16839812—21no—
12#16839701C2211yescharacteristic
13#16839699C411yescharacteristic
14#16839694—21no—
15#16839684—21no—
16#16839673C411yescharacteristic
17C4⋊C4×Dic61—21no—
18#16839613C411yescharacteristic
19#16839609—21no—
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61D411yescharacteristic
28C2×#11758194—21no—
29C2×#11758189—41no—
30M16×D61—24no—
31M16×D61—42no—
32C2×C8×D61—41no—
33Q8×Dic61—41no—
34Q8×Dic61—41no—
35#14519735—41no—
36#14519735—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519706—41no—
51C22⋊#92418—21no—
52C8×Dic61—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×Q8×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—42no—
66C2×Q8×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61SD1612yes—
81C2×C4×D61Q1612yes—
82M16×C61—22no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—42no—
88#11758198—41no—
89#11758198—41no—
90#11758198—42no—
91#11758198—42no—
92C4⋊Dic61—41no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96#11758196—42no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C4×Dic61—42no—
104#11758194—22no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108#11758189—44no—
109C8×D61—44no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61#10312yes—
116Q8×C61—42no—
117Q8×C61—42no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61C2×SD1611yescharacteristic
131C2×C4×C61C2×Q1611yescharacteristic
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#9911yescharacteristic
143C2×Dic61#9911yescharacteristic
144C2×Dic61#10312yes—
145C2×Dic61#10412yes—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—22no—
150C8×C61—42no—
151C8×C61—81no—
152#92418—42no—
153#92418—81no—
154#11721—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61C2×#9911yescharacteristic
158C22×C61C2×#10311yescharacteristic
159C22×C61C2×#10411yescharacteristic
160C2×D61—22no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—42no—
164C2×D61—81no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—42no—
168C4×C61—41no—
169C4×C61—42no—
170C4×C61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—81no—
174Dic61—81no—
175Dic61#32812yes—
176Dic61#32812yes—
177#2396—611no—
178#1742—611no—
179#1458—611no—
180#1354—611no—
181#1354D6111yescharacteristic, complemented
182#1353—611no—
183#1353—611no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61C2×#32811yescharacteristic
187C2×C61#212011yescharacteristic
188C2×C61#213211yescharacteristic
189D61—42no—
190C22×M16—1221no—
191C2×C4×Q8—611no—
192C2×#117—611no—
193#431—1221no—
194#400—611no—
195#399—611no—
196#398—1221no—
197#396—1221no—
198#395C2×D6111yescharacteristic
199#393—611no—
200C4×C4⋊C4—611no—
201C4×C4⋊C4—1221no—
202C4×C22⋊C4—1221no—
203#343—611no—
204#343—1221no—
205#343C2×D6111yescharacteristic
206#324—611no—
207#324C2×D6111yescharacteristic
208#323—1221no—
209C61#1172111yescharacteristic, complemented, Sylow
210C22×Q8C4×D6111yescharacteristic
211C23×C4—611no—
212C2×M16—21no—
213C2×M16—1224no—
214C2×M16—1221no—
215C2×M16—2441no—
216C2×M16—2442no—
217C22×C8—2441no—
218C4×Q8—2441no—
219C4×Q8—2441no—
220#117—2441no—
221#117—2441no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C22×D6111yescharacteristic
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—1221no—
236C2×C42—1221no—
237C4⋊C8—2441no—
238C22⋊C8—21no—
239C22⋊C8—1221no—
240C4×C8—2441no—
241#95—21no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95C4×D6111yescharacteristic
247C24—611no—
248C2×Q8—42no—
249C2×Q8—41no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—611no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1222no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C2×C4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C22×C4D4×D6111yescharacteristic
265M16—22no—
266M16—41no—
267M16—1222no—
268M16—2444no—
269M16—2441no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—2444no—
273C2×C8—2441no—
274C2×C8—2441no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C4⋊C4—2442no—
281C4⋊C4—2442no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C42—1221no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42—2442no—
291C42—2441no—
292C42—2441no—
293C23—612no—
294C23—1221no—
295C23—1221no—
296C23—2441no—
297C23—2441no—
298C23C22⋊C4×D6111yescharacteristic
299Q8—42no—
300Q8—42no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4SD16×D6111yescharacteristic
332C2×C4Q16×D6111yescharacteristic
333C8—42no—
334C8—81no—
335C8—4881no—
336C8—2442no—
337C22—21no—
338C22—21no—
339C22—1222no—
340C22—4881no—
341C22—2442no—
342C22—2441no—
343C22—2441no—
344C22#99×D6111yescharacteristic
345C22#103×D6111yescharacteristic
346C22#104×D6111yescharacteristic
347C4—21no—
348C4—21no—
349C4—42no—
350C4—41no—
351C4—42no—
352C4—41no—
353C4—612no—
354C4—612no—
355C4—4881no—
356C4—4881no—
357C4—2441no—
358C4—2441no—
359C2—21no—
360C2—21no—
361C2—2442no—
362C2#328×D6111yescharacteristic
363C2#2144745711yescharacteristic
364C2#2144750311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11721
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #21443849C2semidirect
5. #21443847C2semidirect
6. #21443845C2semidirect
7. C61×#1354C2semidirect
181. #1354D61semidirect
209. C61#11721semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214490902
#214455562
#214441322
#214438492
#214438472
#214438452
C61×#13542
#1172161